Cosheaves of Steinberg pro-groups

Fuente: arXiv
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Autore principale: Voronetsky, Egor
Natura: Preprint
Pubblicazione: 2023
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author Voronetsky, Egor
author_facet Voronetsky, Egor
contents Steinberg pro-groups are certain pro-groups used to analyze ordinary Steinberg groups locally in Zariski topology. In this paper we show that Steinberg pro-groups associated with general linear groups, odd unitary groups, and Chevalley groups satisfy a Zariski cosheaf property as crossed pro-modules over the base groups. Also, we prove an analogue of the standard commutator formulae for relative Steinberg groups. As an application, we show that the base groups over localized rings naturally act on the corresponding Steinberg pro-groups.
format Preprint
id arxiv_https___arxiv_org_abs_2305_18611
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Cosheaves of Steinberg pro-groups
Voronetsky, Egor
Group Theory
K-Theory and Homology
19C09
Steinberg pro-groups are certain pro-groups used to analyze ordinary Steinberg groups locally in Zariski topology. In this paper we show that Steinberg pro-groups associated with general linear groups, odd unitary groups, and Chevalley groups satisfy a Zariski cosheaf property as crossed pro-modules over the base groups. Also, we prove an analogue of the standard commutator formulae for relative Steinberg groups. As an application, we show that the base groups over localized rings naturally act on the corresponding Steinberg pro-groups.
title Cosheaves of Steinberg pro-groups
topic Group Theory
K-Theory and Homology
19C09
url https://arxiv.org/abs/2305.18611